A solid cylinder of mass rolls without slipping at speed on a horizontal surface

PHYSICS · Single correct · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A solid cylinder of mass

M

rolls without slipping at speed

v

on a horizontal surface. Student A models the cylinder as a single particle and calculates its kinetic energy as

K_A=\frac12 M v^{2}

. Student B treats the cylinder as a rigid system and includes both translation and rotation, obtaining

K_B=\frac12 M v^{2}+\frac12 I\omega^{2}

with

I=\frac12 M R^{2}

. By what factor does Student A’s value differ from Student B’s correct value? (a)

\dfrac12

(b)

\dfrac43

(c)

\dfrac23

(d)

1